The Comparison Of GMC Design And MA Design

Fractional factorial designs are the most used designs in all kinds of experiment designs. For selecting the optimal fractional factorial design, there are a lot of optimal criteria, such as the maximum resolution (MR) criterion, minimum aberration (MA) criterion, clear effect (CE) criterion, general minimum lower order confounding (CE) criterion. These criteria are proposed based on the effect of hierarchy principles. Thus, there are some differences and connections between these optimal criteria. For example, both the MA design and the GMC design are the MR design, and the GMC design has the most clear main effects and clear two factor interactions and so on. So far, there are many articles about MA design and GMC design, such as Zhang, Li, Zhao and Ai(2008), Zhao, Li, Zhang and Karunamuni(2013) and Zhao, Li and Karunamuni(2013) and so on. This paper mainly discusses the similarities and differences between MA design and GMC design. This paper is arranged as follows:The first chapter is the Introduction. It mainly introduces some basic concepts of experimental design, and the basic principles of selecting optimal design and several optimality criteria about experimental design.The second chapter studies the relations and differences of MA design and GMC design in unblocked case. Section2.1summarizes some conclusions in Chen and Cheng (2006). Under some given conditions, although the GMC design and the MA design can be obtained by deleting some columns in the maximum even design, the two designs may be different. Section2.2gets that the GMC criterion has more stronger ability than the MA criterion for discriminating non-isomorphic designs by comparing the word length pattern and aliased effect number pattern. Based on the structures of GMC designs in Li, Zhao and Ai (2011), Section2.3compares the GMC design and the MA design.The third chapter compares the weak MA designs and the GMC designs in blocked case. Firstly, it introduces the blocked MA criterion and B1-GMC criterion. By calcu-lating A2.1of weak MA design, and A2.1of B1-GMC design, if the A2.1does not equal to each other, then the designs under the two criteria are different. The fourth chapter gives a brief concluding.